Commonly assigned U.S. Pat. No. 4,326,803, issued Apr. 27, 1982 and commonly assigned U.S. Pat. No. 4,674,881, issued June 23, 1987 relate to thin film laser gyroscopes, also known as micro-optic gyroscopes (MOGs). It can be shown that the thermal expansion of a MOG waveguide over a typical storage temperature range may cause an uncertainty in the gyro scale factor of the order of 500 ppm. For some applications, such as a spin stabilized projectile rate sensor, this uncertainty is too large. A typical maximum uncertainty that can be tolerated in such an application is only approximately 100 ppm.
For example, an output frequency of a thin film laser gyroscope is given by: EQU Frequency=(4A/(n*Lambda*p))Omega,
where
A =resonator plan area, PA1 n=effective refractive index in the light path, PA1 Lambda=free space wavelength of the laser, PA1 p=resonator perimeter, and PA1 Omega=input rate. PA1 Dp=change in perimeter (Delta p), PA1 alpha=coefficient of linear expansion, and PA1 Dt=change in temperature.
The Scale Factor "S" is given by: EQU S=Frequency/Omega=4A/(n*Lambda*p) Hz/rad/sec, or counts/radian.
For a circular resonator: EQU S=p/(pi*n*Lambda).
If m is the longitudinal mode number, or the number of waves in the ring perimeter, then: EQU m*Lambda=n*p,
and EQU S=m/(pi*n.sup.2).
Typically the value of n is known and, if n is a function of temperature, the MOG substrate temperature can be measured in order to derive a suitable compensation. However, the value of m is typically not well known. When the gyro is switched on the laser will lock to some resonance, the particular resonance depending on the laser's wavelength for peak output, on the width of the gain line, and on the resonators temperature. However, there are typically a large number of ring resonances in the laser's gain width which makes impossible an accurate prediction of which resonance will be selected by a laser locking servo.
It should be noted though that once the laser has locked to the resonator, the scale factor is fixed, and depends only on the value of n. That is, the scale factor is stable but its value is unknown.
A change in optical perimeter due to expansion with temperature is given by: EQU Dp=p*alpha*Dt
where:
For a conventional optical material such as BK7alpha=7 .times.10.sup.-6 /C. Assuming that the temperature varies from -50 to +90C, that is, 20 .+-.70C, assuming a ring having a diameter of approximately 5 cm, so that p =15 cm, letting Lambda =0.8 micron, and letting the waveguide index of refraction =1.5, then: EQU Dp=15.times.(7.times.10.sup.-6).times.70=73.5 micron, and EQU n*Dp=110 micron.
Differentiating Equation (1), EQU Dm=(n/Lambda)*Dp=(1.5/0.8)* 73.5.
Therefore the change in m, or Dm=138 and m=2.8.times.10.sup.5.
Thus, the scale factor variation for a fixed index of refraction is:
DS/S=Dp/p=Dm/m=138/(2.8.times.10.sup.5)=0.0005, i.e. 0.05%, or 500 ppm.
While 0.05% accuracy may be acceptable for certain applications it is not satisfactory for use in a system subject to continuous rates, such as spin-stabilized projectiles. For such a system it can be shown that the scale factor must be known to within a range of 50-100 ppm. This required scale factor range implies that Dm must be ten times smaller than that derived above, that is less than .+-.14 wavelengths.
In other words, each time the laser is switched on it must lock to the same mode number plus or minus 14 wavelengths. However, conventional MOG fabrication materials have an order of magnitude too large a thermal expansion characteristic to provide this range of wavelengths.
One possible solution is to employ a material with ten times lower expansion rate, such as Cervit, as does a ring laser gyroscope (RLG). However, techniques to fabricate the required waveguide structures on Cervit are presently not well characterized. Furthermore, relative to BK7, Cervit is more costly and more difficult to obtain.
Another possible solution is to provide a resonator having a factor of ten times the free spectral range of the typical resonator. However, a single ring resonator would be required to be ten times smaller and, as a result, the scale factor would be reduced as well. For these reasons a reduced diameter single ring resonator is not a viable solution.
In U.S. Pat. No. 4,120,587, Oct. 17, 1978, Vali et al. and in U.S. Pat. No. 4,521,110, June 4, 1985, Roberts et al. describe ring laser gyros in which two independent resonators are constructed. One resonator supports only a CW traveling wave and the other supports only a CCW wave. The intent is to avoid coupling the CW and CCW waves, thus avoiding lock-in. This concept relates only to "active" gyros, the RLG itself, not to a passive type of resonator structure. Furthermore, this technique does not provide a compound resonator.
In U.S. Pat. No. 4,830,495, May 16, 1989, SooHoo et al. describe a passive gyro having two resonators in one material block. The two resonators perform different functions and do not form a compound resonator. Specifically, one resonator forms a laser light source and the other forms a rotation measuring cavity.
In commonly assigned U.S. Pat. No. 4,740,085, Apr. 26, 1988, Lim describes means for compensating active laser gyros for errors caused by differences in CW and CCW beam intensity and by backscatter. His technique relates to a reduction of net backscatter by retro-reflection using external mirrors and does not create a compound resonator structure.
In U.S. Pat. No. 4,632,555, Dec. 30, 1986, Malvern describes the use of a compound resonator for the increase of the overall free spectral range of an active gyro. However, Malvern uses the compound resonator at all times in that he provides the resonator for a gas laser, integral to the resonator. As a result, the resonator is believed to exhibit a lower finesse, due to the losses in the compound resonator construction, with a consequent reduction in laser performance.
It is thus an object of the invention to provide a resonator having having an increased free spectral range without a reduction in scale factor.
It is another object of the invention to provide a compound resonator structure having a free spectral range increased by approximately an order of magnitude over a conventional single ring resonator by coupling together two resonators having a small difference in diameter and without a significant reduction in scale factor.